I wonder if there is a way to ask Safari to clear history when it quits. The shortest setting of this privacy preferences seems to be "keep only the last day". I think it's not enough for privacy matter.

Ok, this not exactly the answer to my actual question, but that's what I wanted to find : no history stored on my computer. Actually, there is a item in the Main Safari Menu named "Private Browsing" that can be checked, and do the job. Nothing is stored nor left on the computer.